Simple Interest vs. Compound Interest: An Overview

Interest represents the cost of borrowing money, added to the principal amount of a loan. Alternatively, when you deposit money in a savings account or certificate of deposit, interest is the reward you earn. Essentially, you are lending money to the bank, and it compensates you with interest.

The interest rate is expressed as a percentage of the principal amount. For example, an interest rate of 4% signifies that 4% of the principal amount is paid or earned as interest.

However, the financial impact of interest can differ greatly depending on whether it is calculated as simple interest or compound interest:

Key Takeaways

• Interest is the cost of borrowing, expressed as a percentage of the total loan amount.
• Simple interest is calculated annually based on the amount borrowed, known as the annual interest rate.
• Compound interest is calculated on the principal plus any previously accumulated interest.
• For instance, daily compounding will result in slightly higher interest payments each day.

Simple Interest

Simple interest refers to the percentage of a loan amount that must be paid annually in addition to the principal. The total interest is determined by the loan’s duration.

To calculate simple interest, use the following formula:

Simple Interest = P × r × n

where:

• P = Principal amount
• r = Annual interest rate
• n = Loan term in years

To determine simple interest, multiply the principal amount by the annual interest rate (expressed as a decimal) and then multiply by the number of years. For example, to convert a percentage into a decimal, divide by 100. Thus, 5% becomes 0.05.

Here’s an example: A student borrows $18,000 at an annual interest rate of 6% for one year. The total interest over three years can be calculated as follows:

Simple Interest = $18,000 × 0.06 × 3 = $3,240

The total repayment amount, including both the principal and interest, is:

Total Repayment = $18,000 + $3,240 = $21,240

Compound Interest

Compound interest involves more complexity. Unlike simple interest, compound interest accumulates over time, meaning you earn or pay interest on both the principal and any previously accrued interest.

Interest can be compounded at various intervals such as daily, monthly, quarterly, semiannually, or annually. More frequent compounding results in higher interest payments or earnings.

The formula for calculating compound interest is:

Compound Interest = P × (1 + r)^t − P

where:

• P = Principal amount
• r = Annual interest rate
• t = Number of years

For instance, if you have a $100 principal amount, an interest rate of 10%, and a period of two years, the calculation would be:

$100 × (1 + 0.10)^2 − $100

$100 × (1.10)^2 − $100

$100 × 1.21 − $100 = $121 − $100 = $21

More Simple Interest vs. Compound Interest Examples

Example 1: Simple Interest

If you invest $5,000 in a 1-year certificate of deposit (CD) with a simple interest rate of 3%, the interest earned in one year is:

$5,000 × 0.03 × 1 = $150

Example 2: Simple Interest

For a 4-month CD with an annual rate of 3%, the interest earned would be calculated as follows:

$5,000 × 0.03 × (4 / 12) = $50

Example 3: Simple Interest

Consider borrowing $500,000 for three years at a 5% simple interest rate. The annual interest payment would be:

$500,000 × 0.05 × 1 = $25,000

Total interest over three years is:

$25,000 × 3 = $75,000

Example 4: Compound Interest

Suppose you need to borrow an additional $500,000 at a 5% annual compound interest rate for three years. The total interest payable can be calculated as follows:

After Year One = $500,000 × 0.05 = $25,000

After Year Two = $525,000 × 0.05 = $26,250

After Year Three = $551,250 × 0.05 = $27,562.50

Total Interest After Three Years = $25,000 + $26,250 + $27,562.50 = $78,812.50

Alternatively, using the compound interest formula:

Total Interest = $500,000 × (1 + 0.05)^3 − $500,000 = $78,812.50

Which Is Better, Simple or Compound Interest?

The choice between simple and compound interest depends on whether you’re saving or borrowing. Compound interest is advantageous for savings as it results in more earnings over time. Conversely, simple interest is preferable for borrowing as it generally results in lower total interest payments.

Simple interest is straightforward to compute. To find the total interest on a loan, simply sum the interest payments for the duration of the loan.

How Do Teens Benefit From Compound Interest?

Younger individuals can greatly benefit from compound interest due to the power of time. Starting to save early allows compound interest to work its magic, with interest accumulating on both the principal and previously earned interest. Regularly adding to savings further enhances earnings.

What is the Rule of 72?

The Rule of 72 is a simple method to estimate how long it will take for an investment to double in value at a fixed annual interest rate. Divide 72 by the interest rate. For instance, with an interest rate of 4%, you divide 72 by 4 to get 18. This means it will take approximately 18 years for the investment to double.

This rule is more accurate for lower rates of return.

The Bottom Line

Compound interest can significantly benefit you, especially if you start saving early. It can substantially increase your savings over time. Conversely, if you’re borrowing money, compound interest can lead to higher total payments. Understanding these concepts emphasizes the importance of saving early and managing debt wisely.